How to build rapport and a connection with a shy girl?

It's discouraging, because shy girls will sometimes act disinterested, and can be confusing. And it's easy to mistake their shyness as disinterest, game-playing or being anti-social and not wanting to talk. So how can I build rapport with a shy girl and get her to open up?
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And I'm at square one, where she'll avoid eye contact often, but I think she likes me 'cause she's flirted and given enough signs.
How to build rapport and a connection with a shy girl?
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